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A Local Property of Large Polyhedral Maps on Compact 2-Dimensional Manifolds

✍ Scribed by S. Jendrol'; H.-J. Voss


Publisher
Springer Japan
Year
1999
Tongue
English
Weight
112 KB
Volume
15
Category
Article
ISSN
0911-0119

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Subgraphs with Restricted Degrees of the
✍ S. Jendrol’; H.-J. Voss πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 276 KB

Let k β‰₯ 2, be an integer and M be a closed two-manifold with Euler characteristic Ο‡(M) ≀ 0. We prove that each polyhedral map G on M, which has at least (8k 2 + 6k -6)|Ο‡ (M)| vertices, contains a connected subgraph H of order k such that every vertex of this subgraph has, in G, the degree at most 4k